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$1.00 Proof

From Mathematics: Algebra , Mathematics: Algorithms
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Due on Jan. 29, 2008
Asked on Jan 28, 2008 at 2:43:37PM

Q:
Prove that the square of any integer a is either of the form 3k or of the form 3k+1 for some integer k. Hint: by the division algorithm, a must be of the form 3q+1 or 3q+2.

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b_h

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$1.00 Squares are either 3k or 3k + 1

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Posted on Jan 28, 2008 at 2:56:56PM

A:
Preview: ... it leaves either a remainder of 1 or 2. If it leaves a remainder of 1 then a = 3q + 1, for some integer q (the quotient). Squaring this we have ...

The full tutorial is about 174 words long .

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techy
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$0.25 complete step by step solution to square of any integer

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Posted on Jan 28, 2008 at 2:59:23PM

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Preview: ... 1 = 3(3a2 + 2a) + 1. Thus n = 3k + 1 for some integer k. Case 3: Suppose n = 3a + 2. Then n2 = (3a + 2)2 = ...

The full tutorial is about 138 words long .